Problem: Solve for $x$ : $x^2 + 3x - 10 = 0$
The coefficient on the $x$ term is $3$ and the constant term is $-10$ , so we need to find two numbers that add up to $3$ and multiply to $-10$ The two numbers $-2$ and $5$ satisfy both conditions: $ {-2} + {5} = {3} $ $ {-2} \times {5} = {-10} $ $(x {-2}) (x + {5}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x -2) (x + 5) = 0$ $x - 2 = 0$ or $x + 5 = 0$ Thus, $x = 2$ and $x = -5$ are the solutions.